Price Informativeness in the Time Series and the Cross Section*

Grace (Haoqing) Fan INSEAD†

haoqing.fan@insead.edu

Peter R. Joos INSEAD

peter.joos@insead.edu

Steven J. Monahan INSEAD

steven.monahan@insead.edu

Sujesh P. Nambiar INSEAD

sujesh.nambiar@insead.edu

This Draft: June 2018

Preliminary and Incomplete Please do not Quote or Distribute without the Authors’ Permission

* We benefited from conversations with Gavin Cassar and Peter Easton. We thank Shuping Chen, Bin Miao and Terry Shevlin for sharing their disclosure-quality proxy with us. † Grace Fan, Steve Monahan and Sujesh Nambiar reside on INSEAD’s Europe campus, which is located at Boulevard de Constance, 77300 Fontainebleau, France. Peter Joos resides on INSEAD’s Asia campus, which is located at 1 Ayer Rajah Avenue, 138676 Singapore.

Price Informativeness in the Time Series and the Cross Section

Abstract

We propose a new measure of price informativeness. Our measure reflects the accuracy of the levels of the expectations embedded in observed equity prices. Hence, it is intuitive yet rigorous. Moreover, it can be used at both the firm- and economy-level and to separately evaluate forecast bias, forecast precision and their combined effect on price informativeness. Our empirical results show that economy-level price informativeness is high when: (1) there is moderate investor sentiment (either positive or negative); (2) limits to arbitrage are low; (3) uncertainty is low; (4) unemployment is low; and, (5) the aggregate earnings-to-price ratio is high. Our firm-level tests show that firms have more informative prices when: (1) they provide more transparency in terms of more-disaggregated accounting data and/or longer 10-Ks or (2) they have good information environments in terms of analyst following and the intensify of that following. Keywords: Price efficiency and price informativeness JEL classification codes: D84, G10, G14 and M40

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1. Introduction

Equity markets play a central role in the economy. They facilitate risk sharing and

intergenerational consumption smoothing. They provide a mechanism for entrepreneurs to obtain

funding; and, they generate price signals that economic agents can use when making real decisions

or determining contractual performance.

The extent to which equity markets fulfill their role depends on price informativeness,

which we define as the degree of accuracy of the expectations of future earnings embedded in a

firm’s current equity market value. When price informativeness is high, investors pay a fair price

for risk sharing and consumption smoothing, entrepreneurs receive funding that is commensurate

with their value-creation potential and prices are informative about economic fundamentals.

With the above motivation in mind, we do two things. First, we propose a new measure of

price informativeness. Second, we provide initial evidence about the determinants of the: (1)

temporal variation in our economy-level measures of price informativeness and (2) cross-sectional

variation in our firm-level measures of price informativeness.

To measure price informativeness, we use the fact that a firm’s equity market value can be

written as a function of its capitalized expected future aggregate earnings (e.g., Easton, Harris and

Ohlson [1992]). Hence, we evaluate the variable , , which equals the difference between firm

’ equity market value at the end of quarter and its capitalized realized aggregate earnings for

the subsequent quarters. (We deflate , by firm ’ equity market value at the end of quarter

and we set 20 quarters.)1 The intuition for , is straightforward: When its magnitude is

1 We evaluate the sensitivity of our results to the value of . In particular, we repeat all of our tests using a value of

28, which is equivalent to seven years. The results of these robustness tests, which are not tabulated, are similar to the results shown in the paper.

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small (large) the earnings expectations embedded in equity market value are more (less) accurate,

and thus price informativeness is relatively high (low).

In addition to being rigorous and intuitive, our measure of price informativeness has two

crucial advantages vis-à-vis alternative extant measures. First, , is a price-based measure not

a returns-based measure.2 This implies that it is a function of the level of equity market value, and

thus it reflects the difference between the level of expected future earnings and the level of ex post

realized earnings. This is important because it is the accuracy of the levels of expectations that

matters. Hence, price-informativeness measures that are based on realized stock returns are

incomplete and possibly misleading. The reason for this is that realized stock returns primarily

reflect changes in expectations; and, even if these changes reflect rational updating on the part of

investors, the underlying level of the expectation may be biased or imprecise. For example, large

positive stock returns may be the result of rational informed traders impounding their positive

private information into price. However, if private and public information are substitutes, or the

amount of unresolved uncertainty remains high, or there are constraints on trading that lead to

asymmetric pricing of good and bad news (e.g., short-selling constraints), etc., the expectations

embedded in price may still be inaccurate.

Second, our price-based measure is determined at the firm-level, Hence, it is more general

than the price-based measure recently developed by Bai, Phillipon and Savov [2016] (BPS

hereafter), which can only be used to infer the average economy-level covariance between current

prices and realized future earnings. , , on the other hand, can be used to evaluate cross-

sectional relations between firm-level characteristics (e.g., disclosure choices) and firm-level price

2 Examples of returns-based price-informativeness measures include synchronicity, which reflects the unexplained variation in realized stock returns (e.g., Morck, Yeung and Yu [2000], Durnev, Morck, Yeung and Zarowin [2003] and Piotroski and Roulstone [2004]) and future earnings response coefficients, which reflect the relation between current realized stock returns and future earnings (e.g., Gelb and Zarowin [2002] and Lundholm and Myers [2002]).

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informativeness. Moreover, we can use temporal variation in the cross-sectional average and

standard deviation of , to evaluate how economy-level forecast bias and forecast precision:

(1) vary across time and (2) covary with other economy-level phenomena such as investor

sentiment, uncertainty, etc.

We begin our empirical analyses by evaluating temporal variation in economy-wide

measures of price informativeness. For each quarter in our sample, we calculate the cross-sectional

average and standard deviation of , , which we refer to as and . These variables

reflect the degree of optimism and precision in investors’ forecasts, respectively. (Larger values

of imply lower forecast precision.) We also calculate the absolute value of , which

we refer to as _ . _ reflects the degree of bias (either positive or negative) in

investors forecasts. Finally, we calculate the variable —i.e.,

root mean squared , . reflects the combined effects of bias and precision, and thus it

is a measure of overall price informativeness.

After calculating the statistics described above we evaluate their temporal associations with

a number of economy-level variables. We begin with the measure of investor sentiment developed

by Baker and Wurgler [2007]. We show that when sentiment is positive: (1) investors’ forecasts

are more optimistic, biased and precise and (2) overall price informativeness is high. However,

when we consider the absolute value of sentiment, we find the exact opposite results. Hence, it is

extreme sentiment, and especially extreme negative sentiment, that is associated with less

informative prices.

Next, we consider the effects of limits to arbitrage and uncertainty. To measure limits to

arbitrage we use the noise measure developed by Hu, Pan and Wang [2013]. We find that when

this measure indicates that there are high limits to arbitrage, investors’ forecasts are more

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optimistic, biased and imprecise. Consequently, and not surprisingly, when there are high limits to

arbitrage, overall price informativeness is low. A similar result holds when there is high

uncertainty as measured by the historical volatility of returns on the S&P 500 index.

We then evaluate the relations between price informativeness and several variables that

reflect the state of the economy: industrial production, unemployment and growth in GDP. We

find weak evidence that price informativeness is pro-cyclical. Specifically, investors’ forecasts

tend to be more optimistic, biased and precise during periods of low unemployment. And, the

precision effect dominates the bias effect causing to be low when unemployment is low.

Finally, we evaluate how informativeness varies with the economy-level book-to-market

and earnings-to-price ratios. We find that, perhaps not surprisingly, when values are high relative

to accounting fundamentals, investors’ forecasts are more optimistic and biased. Moreover, high

price-to-earnings ratios coincide with high , which is consistent with the argument that

divergence between prices and accounting fundamentals is a sign of low price informativeness.

In our second (and final) set of analyses, we evaluate cross-sectional variation in firm-level

price informativeness. To do this we estimate panel regressions of either , or its absolute

value, _ , , on various firm-level characteristics that relate to firms’ disclosure choices

and information environments. By analyzing , we learn about variation in forecast bias

whereas our analyses of _ , provide evidence about variation in forecast precision.

We show that forecast bias is lower for firms that provide more-disaggregated accounting

data and forecast precision is higher for firms that provide more financial information in terms of

longer 10-Ks. We also find that analyst following and the the intensity of that following are each

negatively associated with forecast bias and positively associated with forecast precision. Taken

together, these results are consistent with the common-sense argument that price informativeness

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is higher for firms that make high-quality disclosures or that have “good” information

environments.

We make two contributions. First, we develop an intuitive yet rigorous measure of price

informativeness that reflects the accuracy of the expectations embedded in observed equity prices.

Our measure is flexible and comprehensive in the sense that it can be used to evaluate forecast bias

and forecast precision at both the economy- and firm-level. Second, we provide initial evidence

about the factors that determine temporal variation in economy-level price informativeness and

cross-sectional variation in firm-level price informativeness.

2. Motivation and Contribution

We define price informativeness as the degree of accuracy of the expectations of future

earnings embedded in a firm’s current equity market value; and, higher (lower) accuracy implies

higher (lower) price informativeness. Accuracy is a function of bias and precision. Although biased

forecasts are, ceteris paribus, inaccurate, unbiased forecasts are also inaccurate to the extent that

they are imprecise—i.e., the forecast errors exhibit high dispersion.

Our definition of price informativeness is similar to the definition of fundamental valuation

efficiency described in Tobin [1984] and the definition of forecast price efficiency described in

Bond, Edmans and Goldstein [2012] (BEG, hereafter). As discussed in BEG, price informativeness

overlaps with but is not equal to revelatory price efficiency, which they define as “the extent to

which prices reveal the information necessary for real efficiency.”

Broadly speaking, price informativeness is important for two reasons. First, investors can

use equity securities to smooth their consumption across states and dates (e.g., Arrow [1964]).

Hence, equity prices play a role in determining the amount that investors pay for risk sharing and

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consumption smoothing. To the extent the expectations embedded in equity prices accurately

reflect future payoffs, investors pay a “fair” price, and thus are more likely to achieve optimal risk

sharing and the optimal intergenerational consumption allocation.

Second, price informativeness can have real effects. In the primary market (i.e., the market

for initial public offerings, IPOs), the offer prices determine the amount of funding that

entrepreneurs receive. Hence, when price informativeness is high (low) resource allocations are

efficient (inefficient) in the sense that more funding is given ex ante to entrepreneurs who will

generate larger average payoffs ex post. As discussed in BEG, price informativeness in the

secondary market can also have real effects. If equity prices are informative then, as described in

Hayek [1945], economic agents (e.g., the firm’s managers, its competitors, suppliers, customers,

employees, etc.) can learn from them, and then adjust their real decisions accordingly. Price

informativeness also affects the likelihood that contractual outcomes and regulatory decisions will

be contingent on equity prices (e.g., executive compensation contracts, monitoring the solvency of

financial institutions, etc.). And, to the extent equity prices are used in contracts and by regulators,

price informativeness affects the behavior of contracting parties, regulators and the managers of

the companies being regulated.

Given the important potential consequences of price informativeness, understanding

temporal variation in economy-level price informativeness and cross-sectional variation in firm-

level price informativeness is important. However, obtaining this understanding requires an

empirical approach for measuring price informativeness and, at present, there is no consensus

regarding the best approach. With this in mind, our objective is to add to the extant literature in

two ways. First, we propose a new empirical approach for measuring price informativeness.

Second, we provide initial empirical evidence about the determinants of: (1) temporal variation in

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our economy-level measures of price informativeness and (2) cross-sectional variation in our firm-

level measures of price informativeness.

In the remainder of this section we elaborate on our second contribution—i.e., providing

initial evidence about the determinants of temporal and cross-sectional variation in price

informativeness. We discuss our approach to measuring price informativeness in Section 3.

Determinants of Price Informativeness

There are many factors that determine price informativeness; and, developing an

exhaustive list and evaluating each item on that list is outside the scope of our study. Rather, we

identify four general determinants. The first is uncertainty, which is the root cause of price

uninformativeness. Specifically, if there is no uncertainty, investors will make perfect forecasts

and prices will be fully revealing. However, when there is uncertainty, investors forecasts will be

imprecise and possibly, but not necessarily, biased.

The second general determinant relates to firms’ information production decisions. Ceteris

paribus, firms that produce more information will have higher price informativeness. The third

general determinant relates to investors’ information-acquisition decisions and the manner in

which they process the information that they acquire. Ceteris paribus, when investors conduct

more private information acquisition, their forecasts are more precise and price informativeness is

higher. Moreover, to the extent that investors process the information they acquire in a rational

manner, their forecasts are unbiased and more precise, and prices are more informative.

The final general determinant of price informativeness that we discuss is trading

constraints. The quintessential example of a trading constraint is a prohibition on short selling. As

discussed in Miller [1977], short selling is a way for investors to profit from negative private

information—i.e., private information that implies that the current price is too high. Consequently,

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a prohibition on short selling will cause the expectations embedded in price to be biased upwards.

Trading constraints can also arise endogenously. For example, high uncertainty and information

asymmetry can lead to illiquidity that acts as a de facto constraint on trade. Regardless of their

origin, trading constraints typically imply lower price informativeness.

With the above discussion in mind, we make three observations. First, the determinants of

price informativeness are related and interdependent. For example, as discussed in Beber and

Pagano [2013], high uncertainty, concerns about firms’ information production decisions and

biased information processing motivated numerous regulators to impose short-selling constraints

during the 2007-2009 global financial crisis. Second, it is likely that there is endogeneity between

price informativeness and the different determinants that we identify. For example, managers who

perceive their firm’s shares to be mis-valued may react by disclosing more information, which, in

turn, affects the accuracy of the forecasts embedded into price. Finally, we do not argue that our

discussion of the determinants of price informativeness is exhaustive. Rather, we simply seek to

fix ideas and motivate our empirical tests in which we explore the relation between our measures

of price informativeness and various phenomena.

3. Measuring Price Informativeness

Our measures of price informativeness are motivated by the following expression for firm

’ equity market value at the end of quarter , , :

,∑ , , , , , , , |

,

, ∆ , |

, (1)

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In equation (1), ∙ | is the expectation at the end of quarter conditional on the information

available at that time, which we denote as . , is firm ′ earnings for quarter and

, is the dividend paid by firm at the end of quarter . , is firm ’ equity book value

at the end of quarter . , 1 , and , 1 , ; and, , and , are the quarterly

risk-free rate and the expected quarterly rate of return on firm ’ equity capital, respectively.

Finally, , ∑ , , 1 , is firm ’ aggregate cum-dividend

earnings for the time period spanning quarter 1 through and

∆ , , , , , , , , , is the change in

the premium of equity market value over equity book value.

Equation (1) is not new to the literature. Rather, as shown in Easton et al. [1992], if we

assume that dividends are paid out of excess cash that the firm would have invested in risk-free

bonds and , is non-stochastic, , 1 , 1 is equal to the following:3

, 1, ∑ , , , |

, (2)

Finally, if we also assume clean-surplus accounting in expectation, which implies that

, , | ∑ , , | , equation (1) follows directly from

equation (2) and vice versa.4

3 The term ∑ , , in equation (2) is necessary to preserve dividend-policy irrelevance per Miller and Modigliani [1961]. That is, holding the firm’s investment opportunities constant, the expected change in value is the same regardless of whether the firm pays a dividend or withholds the funds and invests them in risk-free bonds.

4 In particular, , 1, ∑ , , , |

,

⇒ ,, ∑ , , , , , , , |

,

, , ∑ , , , , , , |

,

∑ , , , , , , , |

,

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In addition to being consistent with first principles, equation (1) motivates an intuitively

appealing approach for measuring price informativeness: Compare ex ante equity market value to

the capitalized ex post realized value of , . In particular, we calculate the following variable,

which we refer to as , :

,

,,

,

, (3)

There are two key issues with using , as a measure of price informativeness. Below we

describe each issue and how our empirical design addresses it.

Ignoring ∆ ,

, is only a function of , and , —i.e., we ignore ∆ , . The advantage of

ignoring ∆ , is that it is a function of the realized value of , , , which equals the

revision in investors’ expectations during the time period spanning quarters through .

However, if investors are rational, revisions in their expectations are, by definition, unpredictable.

Hence, ignoring ∆ , allows us to ignore the effect of unpredictable “noise” on our

inferences about price informativeness at quarter .

There are two disadvantages to ignoring ∆ , . First, if investors are not fully rational,

revisions in their expectations reflect both unpredictable noise and price uninformativeness.

Consequently, a disadvantage of ignoring ∆ , is that we ignore some of the variation in price

informativeness attributable to irrational information processing at time . That said, to the extent

that irrational information processing leads to biased or imprecise forecasts of , , not all of its

effect on price informativeness is lost.

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The second disadvantage of ignoring ∆ , is truncation bias. That is, ignoring

∆ , can cause us to infer that price informativeness is low when it is not. The reason for this

is that , only reflects the portion of value created (or destroyed) after quarter that is captured

by the accounting system during the time period spanning quarters through . Hence, if at

time investors accurately predict future events that create (or destroy) value but these events do

not affect , , , will be confounded. Moreover, because accounting earnings tend to

recognize good news with a lag (e.g., Basu [1997]) and are understated for firms that experience

growth in expenditures that are accounted for conservatively (e.g., Zhang [2000]), even events that

occur before quarter may not be fully captured by , .

Dealing with truncation bias involves making a tradeoff. On the one hand, larger values of

of are better in the sense that there will be less truncation bias. However, because , is a

function of ex post realizations, increases in lead to decreases in the sample size. With this

tradeoff in mind, we choose to set 20 quarters (i.e., five years). We do this for two reasons.

First, as discussed in Koeva [2000], investment plans tend to take roughly two years to implement.

Hence, a five-year period will capture the effects of investment plans initiated in year as well as

a portion of the effects of plans initiated between year and year 3.

Second, to calculate , we obtain ex post realizations of earnings and dividends from

Compustat; and, the Compustat files that we use only have data for fiscal quarters ending on or

before December 2016. Hence, by choosing 20, we can observe price informativeness for

quarters up to December 2011. Consequently, we can evaluate the behavior of price

informativeness during the period around the global financial crisis of 2007 through 2009.

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Bias versus Precision

Low price informativeness does not necessarily imply that the sign of , will be either

positive or negative. The reason for this is that, if investors are rational, their conditional

expectations are unbiased even when they have low-quality information. Consequently, there is no

clear relation between the sign of , and degree of price informativeness. Moreover, the time-

series and cross-sectional averages of , can be close to zero despite the fact that prices are

based on imprecise forecasts. We address these issues in two ways. First, when the unit of

observation is measured at the firm-quarter level, we evaluate both , and its absolute value—

i.e., , , which we refer to as _ , . We evaluate , because it is informative about

the degree of bias embedded in investors’ forecasts. _ , , on the other hand, is informative

about the precision of those forecasts. In particular, higher values of _ , imply lower

precision.

Second, when the unit of observation is measured at the economy level, we evaluate the

temporal behavior of the cross-sectional average and standard deviation of , , which we refer

to as and , respectively. We evaluate because price informativess is a function

of both the quality of the information available to investors and how they process that information.

For example, investors may exhibit excess optimism in some time periods and excess pessimism

in others. This, in turn, implies that the cross-sectional average of will vary over time. We

evaluate because it is informative about the precision of investors’ forecasts. In particular,

higher values of imply less precise forecasts and lower price informativeness, ceteris

paribus. Finally, we also evaluate temporal variation in root mean squared , , which we refer

to as . This is a comprehensive measure that reflects the combined effects of bias and

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precision. Specifically, . Hence, higher values of

imply lower overall price informativeness.

Comparison to Extant Approaches

Ignoring our approach, there are three commonly-used extant approaches for measuring

price informativeness. The first is often referred to as synchronicity and it is motivated by empirical

results shown in Roll [1988]. He estimates regressions of realized firm-level stock returns on

contemporaneous “authenticated” information (e.g., the realized return on the market portfolio, the

realized return on a size- and industry-matched portfolio, etc.) and he finds that the average of the

r-squareds from these regressions is roughly 35 percent for monthly data and 20 percent for daily

data.

An interpretation of Roll’s results is that high unexplained stock return volatility is

attributable to rational, informed traders impounding their unobservable, private information into

price. Hence, as discussed in Morck et al. [2000], Durnev et al. [2003] and Piotroski and Roulstone

[2004], low synchronicity between a firm’s stock returns and contemporaneous returns on various

portfolios (e.g., the market portfolio and/or an industry-matched portfolio, etc.) can be interpreted

as an indicator of high price informativeness.

Using synchronicity to measuring price informativeness has two limitations. First, as

discussed in Roll [1988] and West [1988], an alternative interpretation of low synchronicity is that

it reflects excess volatility attributable to either “frenzies” or uninformed noise trading. Second,

even if low synchronicity is the result of informed traders impounding their private information

into price, it is not necessarily synonymous with high price informativeness – at least, not as we

define it. High informed trade could be accompanied by high uncertainty, private information and

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public information might be substitutes, etc. Consequently, low synchronicity could reflect rational

updating of expectations that are, nonetheless, relatively imprecise and biased.

The second commonly-used approach for measuring price informativeness is to evaluate

future earnings response coefficients, FERCs (e.g., Gelb and Zarowin [2002] and Lundholm and

Myers [2002]). A FERC is the slope coefficient on “future” earnings obtained from a cross-

sectional regression of annual realized stock returns for year on earnings reported in years

subsequent to year . The argument is that higher FERCs imply greater price informativeness.

However, this interpretation is not obvious. As shown in Vuolteenaho [2002], realized stock

returns reflect changes in expectations about future earnings. However, price informativeness

relates to the properties of the levels of the expectations; and, a high correlation between changes

in expectations and realized future earnings does not necessarily imply that the levels of those

expectations are unbiased and precise.

The final alternative price-informativeness measure that we discuss is the one described in

BPS. They measure price informativeness as the slope coefficient from a cross-sectional regression

of annual realized earnings for year on equity market value at the end of year .5 They

consider horizons (i.e., values of ) between one and five years and interpret higher slope

coefficients as an indication of higher price informativeness. This approach overlaps with ours in

the sense that BPS evaluate prices, which reflect levels of expectations, and not returns, which

reflect revisions in expectations. Nonetheless, it has two limitations. First, BPS’ measure can only

be used to evaluate temporal variation in economy-level price informativeness. Our approach, on

the other hand, generates measures of both economy- and firm-level price informativeness. Hence,

5 BPS deflate both variables by total assets at the end of year .

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we can evaluate how price informativeness varies with firms’ disclosure choices, investors’

information acquisition decisions, etc.

Second, the approach developed by BPS relates a firm’s price at the end of year to a

single earnings realization for a particular subsequent year . Hence, in order to evaluate

multiple horizons, a separate regression must be estimated for each horizon, and then the

coefficients from the separate regressions must be combined. However, there is no obvious way

to do this. We circumvent this issue in the natural way: We use the fact that earnings aggregate

over time. In particular, we use , , which equals a firm’s aggregate cum-dividend earnings for

the entire time period of interest, as our earnings measure. Using , also reduces the influence

of any specific year. For example, suppose a firm manipulates its reported accruals in quarter

. Under accrual accounting, this manipulation will eventually reverse and, if that reversal

occurs in quarter , there is no effect on either , or our inferences about price

informativeness.6

Summary

Our approach to measuring price informativeness is intuitive yet rigorous. It provides

evidence about the bias and precision of the levels of the expectations embedded in observed equity

market values. The measures derived from it are comprehensive in the sense that they reflect the

combined effects of uncertainty, firms’ information production decisions, investors’ information-

acquisition decisions and information-processing, and trading constraints. Moreover, they can be

used to evaluate variation in both economy-level and firm-level price informativeness.

6 A third advantage of using , is that it is a cum-dividend measure; hence, it preserves dividend policy irrelevance.

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4. Data, Sample and Descriptive Statistics

Data and Sample

We obtain our data from several sources. We collect our fundamental accounting data from

Compustat. To construct our initial sample, we consider the time period between 1975 and 2016

inclusive; and, we include all firm-quarter observations in the database that are US-incorporated

and not ADRs. We exclude firms that do not have a calendar quarter fiscal year-end and firms that

only have semi-annual reporting frequency. Our full sample does not exclude financial services or

utility firms. We trim this initial sample using the following rules. First, we remove firm quarters

with , , , (total assets) or , (total liabilities) that are either missing or not greater

than zero. We also remove firm quarters that have a stock price that is less than or equal to one

dollar. Next, we adopt a set of additional trimming rules related to fundamental accounting

variables (see Appendix A for all variable definitions). We require return on equity, , , and,

return on assets, , , to each be between four and negative four; profit margin, , , to

be below one; and, , to be between one and 20. In Appendix B, we describe how we

calculate , , our key price informativeness measure. We remove observations with extreme

values of , . In particular, for each quarterly cross-section we delete observations for which

, is either below the first percentile or above the 99th percentile of the cross-sectional

distribution of , . Our exclusion and trimming procedures result in the elimination of 444,058

firm-quarters (331,318 because of missing values and 112,740 attributable to our filters) leading

to a main dataset of 473,569 firm-quarter observations, covering 148 quarters.

We use this main dataset as the data source for two sets of tests. First, we perform time-

series analyses of economy-level measures of price informativeness. For each quarterly cross-

section, we create economy-level measures of price informativeness by aggregating the firm-level

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price informativeness measures for that quarter. This leads to a sample of 148 quarterly

observations. Next, we perform firm-level cross-sectional analysis by using the firm-year sample

that is a subset of the main dataset. In particular, we extract all quarters from the main dataset that

relate to the fourth fiscal quarter, and then we obtain annual data for the corresponding fiscal year.

We then match these observations with firm-level informativeness measures estimated two

quarters ahead, i.e., , and _ , . This ensures that our price informativeness

measures reflect the annual accounting information from the most-recent fiscal year. This

procedure leads to an initial sample of 125,471 firm-year observations. We trim this sample at the

top and bottom one percentile based on the value of , , removing 9,818 observations.

Finally, we require availability of all control variables in the firm-level regressions, leading to a

final firm-year sample with 79,382 observations.7

5. Time-series Analyses

In our first set of analyses we study the temporal variation in price informativeness at the

economy-level over our sample period. In these analyses, we consider the three price

informativeness measures mentioned in Section 3: , and . We also compute

an additional variable, _ , which equals the absolute value of . Vis-à-vis ,

_ is a better indicator of the implications of biased forecasts for price informativeness.

The reason for this is that, holding the magnitude of constant, its sign is irrelevant in the

sense that positive implies the same level of uninformativeness as negative .

Nonetheless, we also evaluate because it sheds light on the extent to which investors’

7 Note that availability of some of the disclosure variables of interest will further constrain the sample. See Section 6 below.

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forecasts are either optimistic or pessimistic. In Appendix A we present the detailed definitions of

the variables and in Appendix C we describe how we aggregate firm-level measures to calculate

the quarterly measures that we use in our time-series analyses.

To study the temporal variation in the price informativeness variables, we explore their

association with several economy-level variables. We start by including the sentiment index from

Baker and Wurgler [2007]. Baker and Wurgler [2007] describe how investor sentiment in markets

can affect the extent to which prices reflect fundamentals of stocks, in particular for so-called

harder-to-arbitrage stocks. They develop a sentiment index and find empirical evidence that this

index not only relates to current stock returns, but also helps predict returns across different

categories of stocks. We include the sentiment index from Baker and Wurgler [2007] in two ways:

measures the signed index as defined by Baker and Wurgler [2007]; and, is the

absolute value of . We distinguish between and because they potentially

influence price informativeness differently: Although is directional, reflects the

extent of sentiment in the market, regardless of its direction. In other words, larger values of

capture whether investors are more exuberant or gloomy relative to being more

“neutral.”

Next, we include the noise index, , developed by Hu et al. [2013] to capture a broad

measure of market-wide liquidity. As discussed by Hu et al. [2013], this broad measure of noise

connects with the amount of arbitrage capital available in the market and, as the name of the index

suggests, this amount will affect the extent to which information enters into market prices through

trading (see also BPS). We further include an additional metric of market uncertainty in our design,

namely , which is the standard deviation of the daily returns on the S&P 500 measured

during the last month of the quarter. We opt for this metric as opposed to the more traditional

20

metric of the VIX index because observations for the VIX, as it is currently measured, only go

back to 2003. In untabulated analysis, we observe a strong correlation between our metric

and the VIX index (the Pearson correlation is 0.87).

Next, we focus on three metrics of “real” economic activity: industrial production,

, the level of unemployment, , and realized GDP growth .

We include these variables for two reasons. First, Chen, Roll and Ross [1986] examine the

influence of economic “state” variables on asset prices and stock market returns. They find that

innovations in a number of these state variables are priced in the market and reflected in stock

returns. By considering the relation between the levels of these economic variables and our

measures, we aim to understand whether the time-series variation of our metrics at the aggregate

level is a function of the business cycle. Second, we introduce these variables as complements to

the sentiment index proxy. As Baker and Wurgler [2007] discuss, their sentiment index

components have been orthogonalized relative to a set of macro-economic indicators. Finally, we

focus on the aggregate book-to-market, , and earnings-to-price, , ratios. We include both

variables so that we can evaluate whether the time-series variation in our informativeness measures

is associated with changes in valuation multiples that reflect the premium of current price vis-à-

vis current accounting fundamentals.

We report the results of the time-series analyses in Tables 1 through 4. Table 1 reports

descriptive statistics on both the main price informativeness variables and the macro variables.

Panel A shows that is positive during our sample period (the average is 0.69 and the median

0.78). Further, there is considerable variation in , _ , and .

Importantly, since we observe a time-trend in our main variables of interest, we detrend them when

21

we study their association with the macro variables.8 (We also detrend the macro variables.) Panel

B shows descriptive statistics on the detrended variables. As shown in Panel B, exhibits

more positive deviations from the sample time-trend, whereas a majority of the detrended

_ observations are negative. and also show significant variation across

the sample period. Panels C and D show both the raw values and the detrended values for all the

macro variables. We observe in Panel C that over the sample period is on average positive,

while shows significant variation, suggesting that over the period investor sentiment

exhibited wild swings. Similarly, both panels show that the other macro variables also exhibit

strong variation across the sample quarters.

In Table 2 we present univariate correlations between the price informativeness variables

across the sample quarters. The table shows a strong correlation between and _ .

This strong correlation relates to the fact that, per Panel A of Table 1, tends to be positive,

and thus there is a lot of overlap between it and _ . The fact that is typically

positive is likely a manifestation of truncation bias. Importantly, the Pearson correlations in Table

2 show that both and _ are negatively correlated with and . The

latter two metrics therefore appear to capture different phenomena from the bias metrics. Further,

there is high positive correlation between and , which implies that, vis-à-vis bias,

precision is the dominant determinant of overall price informativeness as measured by .

Table 3 presents the univariate correlations between the macro variables in our design. Not

surprisingly, we observe that a number of these variables are correlated over time.

8 To verify the presence of a time trend we construct the variable _ , which equals one in the first quarter of our dataset, and then it increases by increments of one until it reaches its maximum value of 148. We observe that that correlation between each of the price informativeness measures and _ is roughly 0.70. Similarly, five out of the nine macro variables exhibit correlations with _ above 0.70. Consequently, we detrend each variable by separately regressing it on _ , and then using the residuals from the regression as our detrended variables of interest.

22

We present our main time-series results on Table 4. These are univariate correlations

between the price informativeness variables and the individual macro variables. The table presents

both Pearson and Spearman correlations, which are similar. Hence, we focus our discussion mainly

on the Pearson correlations in Panel A. To start, is positively correlated with and

_ but negatively correlated with and . This implies that investor

sentiment is positively associated with the level of optimism, degree of bias and the level of

precision. Moreover, per the negative correlation between and , the precision effect

dominates the bias effect so that overall price informativeness is increasing in the level of investor

sentiment.

On the other hand, is negatively correlated with and _ but

positively correlated with and . Hence, extreme (positive or negative) investor

sentiment is associated with less optimistic forecasts that are less biased but also less precise. And,

the precision effect dominates so that overall price informativeness is lower when sentiment is

extreme. Taken together, the results for and suggest that positive sentiment and

extreme sentiment are different phenomena. In particular, it is extreme sentiment, and especially

extreme negative sentiment, that is associated with less informative prices.

exhibits a positive correlation with both bias variables (Spearman only),

and . This suggests that limits to arbitrage are associated with relatively optimistic

forecasts, that are more biased and less precise, and thus lower price informativeness. is

uncorrelated with the bias variables but exhibits a positive correlation with and .

Hence, when economy-level uncertainty is high (low), investors make less (more) precise forecasts

and price informativeness is lower (higher).

23

The correlations between the state variables—i.e., , and

—and the informativeness measures are mixed. The bias variables are negatively

correlated with , which in turn, is positively correlated with and . Hence,

when the economy is good in the sense that unemployment is low, investors tend to make forecasts

that are more optimistic, more biased and more precise; and, the precision effect dominates the

bias effect so that price informativeness is high. This last result is reinforced by the fact that

exhibits negative (but weakly significant) Pearson correlations with and

. However, is not associated with either or and it exhibits

a somewhat counter-intuitive negative association with both and _ . Taken

together, these results weakly suggest that price informativeness is pro-cyclical.

Both the book-to-market and earnings-to-price ratio are negatively correlated with each of

the bias measures. This is consistent with the notion that high aggregate price multiples are

observed in time periods when investors are biased and relatively optimistic. However, the two

ratios exhibit different relations with precision. is positively correlated with . This

implies that investors make more precise forecasts when market prices are high relative to the

accounting fundamentals. Moreover, this precision effect offsets the bias effect so that there is no

relation between and . On the other hand, and are uncorrelated. Hence, the

negative relation between and _ leads to a negative relation between and

, , which, in turn, suggests that high prices relative to current fundamentals coincide with

time periods when optimism and bias are high and price informativeness is low.

Overall, the results in Table 4 indicate that during our sample period several macro

variables are associated with our aggregate metrics of price informativeness. Our findings

complement those in BPS and Farboodi, Matray and Veldkamp [2017] who jointly document a

24

broad rise in price informativeness for S&P 500 firms but not for the overall economy. Our

analyses show that macro-variables are associated with price informativeness measures for a broad

sample of firms, comprising S&P 500 and other firms. We now turn to firm-level analyses to

examine the cross-sectional variation in firm-level price informativeness.

6. Firm-level Cross-sectional Analyses

In our second set of analyses we study cross-sectional variation in firm-level price

informativeness. Building again on our discussion in Section 3, we consider two firm-level price

informativeness variables, , and _ , (see Appendix A for precise definitions).

, is our firm-level measure of forecast bias and _ , (i.e., the absolute value of

, ) is our firm-level measure of forecast precision. (Higher values of _ , imply low

precision.) We evaluate the association between these two variables and a selection of cross-

sectional variables that relate to firms’ disclosure practices and information environments.

We start by including three proxies for disclosure quality. Our first proxy, , , is

obtained from Chen, Miao and Shevlin [2015]. , is a measure of disclosure quality that gauges

the level of disaggregation of the financial data in a firm’s annual report. The underlying idea is

that greater disaggregation leads to greater transparency. Chen et al. [2015] validate this claim by

studying the relation between their metric and analyst forecast properties, bid-ask spreads and

estimates of cost of equity. Our second metric of disclosure is the fog index, , , from Li

[2008]. This disclosure metric differs from , as it measures the “readability” of financial

reports and does not simply gauge the level of disaggregation of quantitative items. Li [2008]

introduces the measure to the literature and shows how it relates to firm performance and earnings

persistence. The latter is important from a forecasting perspective as it implies that readability of

25

annual reports is associated with more sustainable earnings that may be easier to forecast, which,

in turn, could affect price informativeness. Recent work by Loughran and McDonald [2014],

however, criticizes the fog index as being misspecified and hard to measure. Instead these authors

propose a separate readability metric, namely the file size of the 10-K. We use this metric, which

we refer to as 10 , , as our third disclosure proxy. The analysis in Loughran and McDonald

[2014] shows that larger 10-K file sizes are associated with larger abnormal return volatility, higher

absolute unexpected earnings and higher analyst dispersion. They interpret these results as

implying that large 10-Ks lead to “information overload,” and thus less informed prices.

Next, we include two variables that measure analyst activity for a given firm. We include

these analyst-based variables since “analysts’ forecasts have the potential to influence asset prices

by conveying information about future cash flows and about the discount rates applied to future

cash flows.” (Kothari, So and Verdi [2016]). The presence of analyst coverage therefore is likely

an important component of the information environment of the firm. Our measure ,

measures whether a firm is covered by analysts, while , measures the intensity of

the analyst following for a firm.

We also include a number of control variables in the regressions. Per Akbas [2016], we

include , in the regression to control for short-sell constraints. We also include

, to capture the R&D intensity of the firm. We include this variable for two reasons.

First, R&D spending is a partial control for truncation bias. In particular, given that R&D

expenditures are immediately expensed, as discussed in Zhang [2000] and Monahan [2005],

earnings will be low (high) when growth in R&D spending is high (low). Additionally, larger R&D

26

activity could be an indicator of increased uncertainty about the firm’s future.9 Next, based on the

work by Chang et al. [2018], we include the variable , , which is a firm-specific

forecast of the conditional standard deviation of , . We include this variable because it

reflects the level of uncertainty about the firm’s future earnings, which should have both a direct

effect and indirect effect on price informativeness. Regarding the direct effect, ceteris paribus,

higher uncertainty implies lower precision and lower price informativeness. However, if

management responds to this uncertainty by providing more information, there will be an

offsetting indirect effect. By including , in our regressions we partially control for

the fact that manager’s disclosure choices are endogenously determined.

Finally, we insert four additional control variables. To control for risk, we include the

firm’s factor loadings on the two Fama-French [1993] risk factors that relate to market to book

and size, which we refer to as _ , and _ , , respectively. We also control for

a firm-specific forecast of the conditional mean of , , per Chang et al. [2018]. We insert

this control for expected firm performance in the specification to address the fact that firm

performance may be a determinant of firms’ disclosure decisions and investors’ information

acquisition decisions. Our final control variable is , , which controls for the extent to which

the clean surplus assumption is violated during the five-year horizon over which we measure

, .

Based on the above discussion, we estimate the following regression:

, _ , , , ∑ , , , , , (4)

9 Barth, Kasznik, and McNichols [2001], among others, relate the presence of intangibles (e.g., investing in brands, R&D) to the difficulty of the forecast setting.

27

In equation (4), , , is one of the five variables of interest (disclosure or information

environment) and , , is one of the seven control variables. We measure , and

_ , two quarters after the fiscal-year end for all observations. Our regression

specifications also include industry θ (based on the Fama-French 12 industry classification) and

year ϑ fixed effects. We calculate standard errors using double-clustering on industry and year.10

Tables 5 through 7 present our findings of the cross-sectional analyses. The descriptive

statistics in Table 5 show that all variables exhibit considerable variation across the sample,

reflecting the broad cross-section of firms we have included. As before, we observe that , is

predominantly positive in the sample: its mean (median) is 0.81 (0.68) and the 25th percentile is

positive. This also implies that there is a large overlap between , and _ , . The

disclosure variables , , , and 10 , show high variation across the sample. Further,

more than half the firms in the sample have no analyst following, consistent with our sample

representing a broad cross-section of firms. Other notable statistics are that , is

about 34 percent on average and about 25 percent of firms report non-zero R&D spending; and,

the forecast of the conditional mean of , , , , is positive on average and for

the typical firm (the mean and median are 0.07 and 0.11, respectively).

We show univariate Pearson and Spearman correlations in Table 6. Focusing specifically

on the first two columns in the table, we observe that both , and _ , exhibit

significant correlations with the variables of interest and the control variables in the regressions.

Consistent with the earlier observation in Table 5 that most , observations are positive, we

further observe a strong correlation between , and _ , . Focusing on the three

10 We winsorize several variables in order to reduce the effects of outliers. The variables , and , are winsorized at the top and bottom one percentile, and the variable , is winsorized at the 95th percentile.

28

disclosure variables, we note first that, perhaps surprisingly, , is positively correlated with

, and _ , . Further, the two “readability” metrics correlate differently with ,

and _ , . A higher FOG index suggests more biased and lower precision but the presence

of longer 10-Ks points in the other direction: reduced bias and higher precision. The presence of

analysts ( , ) does not correlate with , but is correlated negatively with

_ , ; and, the intensity of analyst following is correlated negatively with both , and

_ , . In sum, the patterns of the univariate correlations between , or _ , and

the main variables of interest present a few surprising results. Of course, these univariate

correlations ignore potential confounding influence of other variables. We therefore now turn to

the regression tests.

Table 7 presents the results of the regression specifications. Panel A (B) shows the findings

for the regressions that focus on , ( _ , ). Given the strong overlap between these two

variables, the findings in both panels are similar.11 We therefore discuss both sets of results

simultaneously and highlight differences where they exist. First, there is a significant negative

relation between , and both , and _ , . This implies that forecast bias is lower

and forecast precision is higher for firms that provide more-disaggregated financial statement data.

These results are consistent with the findings in Chen et al. [2015]. However, the coefficients on

both , and 10 , are insignificant suggesting that “readability” is not associated with

price informativeness.

Regarding analyst following, the results on Panel A suggest that it is not associated with

forecast bias whereas the results on Panel B suggest that forecast precision is higher for firms that

11 The overlap creates the concern that _ , does not pick up precision of the forecasts but rather shows bias. We address this concern below.

29

are followed by analysts. The intensity of analyst following also appears to matter. In particular,

the coefficients on , are significantly negative in both Panels A and B. To the

extent that analyst following and the intensity of that following are positively associated with the

quality of firms’ information environments, these results imply that a better information

environment is associated with higher price informativeness (i.e., lower bias and higher precision).

Focusing on the other variables, we observe some additional striking patterns. First, the

coefficients on , are significantly negative in both Panels A and B. These results

are consistent with the argument that, when institutional holdings are high, short-sell constraints

are low (e.g., Akbas). Consequently, the forecasts embedded in stock prices are less optimistic

(Panel A) and more precise (Panel B). The coefficients on , are positive and highly

significant, consistent with a positive (negative) association between R&D spending and forecast

bias (precision). The former finding is consistent with , reflecting truncation bias in

, . The positive coefficient on , across specifications suggests that higher

earnings uncertainty is positively associated both with higher bias and lower precision.

Finally, regarding the other control variables, we find that the coefficients on the Fama-

French factor loadings are generally not significant across specifications. This alleviates the

concern that cross-sectional variation in our price informativeness proxies is simply a

manifestation of cross-sectional differences in risk. Also, the negative coefficients on

, across specifications is consistent with lower positive bias and higher precision

when expected , is higher. Finally, for completeness, the control variable , tends to

be associated with higher bias and lower precision.

Although the findings in Panel A and B of Table 7 suggest that our variables of interest are

associated with bias and precision, there is an important caveat. As discussed above, there is a lot

30

of overlap between , and _ , . This overlap is likely attributable to two features of

our research design: (1) truncation of the forecast horizon to 5 years and (2) our assumption about

the equity risk premium – see Appendix B. Truncation bias clearly leads to upwards bias in , .

Moreover, to the extent our estimate of the equity risk premium is too high, , will be biased

upwards. The important implication of the overlap is that our metric _ , may not reflect

precision; rather, it may simply be a redundant measure of , .

We therefore carry out one additional set of tests to evaluate precision of the price forecasts.

We follow a two-step process. First, we estimate specification (1) in Table 7 Panel A and obtain

the residuals from this regression. Next, we take the absolute values of these residuals and regress

them on the specifications in columns (2) through (6) of Table 7 Panel A. This two-step process

provides a better assessment of the relation between our variables of interest and the precision of

the price forecasts. By taking the absolute values of the residuals from the first regression, we

obtain a distribution of firm-specific absolute deviations from our estimate of the firm-specific

conditional mean obtained from regression (1). In other words, this distribution captures the

relative unsigned magnitude of a measure of , that has been debiased. By regressing these

absolute deviations on the treatment and control variables, we evaluate how the variables of

interest relate to the level of imprecision.12 That is, a negative association implies higher precision.

We report the descriptive statistics of the residuals, , , and their absolute values,

_ , , in Table 5. We observe that more than half of the observations have a negative

value of , , which implies that , tends to exceed the conditional mean more often

12 We replicate the analysis by estimating the different specifications (2) through (6) from Table 7 Panel A separately to obtain separate sets of residuals for each regression. We then regress the absolute values of these residuals in the second stage on the same specifications. This approach generates similar results to the ones that we report in the paper.

31

than it falls below it. (The average value of , is, by construction, equal to zero.) More

importantly, as shown on Table 6. The correlation between _ , and , is only

0.41; hence, _ , contains different information than , .

In Panel C of Table 7, we show the results from the second-stage regressions. We observe

that the coefficient on , is statistically insignificant. Taken together with the results in Panel

A, this result suggests that the positive relation between disaggregation and price informativeness

is solely attributable to a reduction in bias. The coefficient on , remains insignificant, but

10 , now obtains a significantly negative coefficient. This implies that a longer 10-K file

is associated with more precise forecasts. This finding may be surprising given the discussion and

findings in Loughran and McDonald [2014]. However, they focus on short-term outcome variables

such as abnormal return volatility around the publication of the 10-K whereas our measure of price

informativeness is based on the level of the equity market value measured well after the date on

which the 10-K is published. Consequently, the results are not necessarily contradictory. In

particular, as discussed in Loughran and McDonald [2014], longer 10-Ks may lead to short-term

information “overload.” However, longer 10 Ks may also be more informative, which implies that,

to the extent investors eventually “digest” this information, longer 10-Ks are associated with more

informative prices. The results on both analyst variables remain unchanged—i.e., both the

presence of analysts and the intensity of their forecasts improves the precision of forecasts.

Turning to the other variables, the coefficients on , are significantly

negative. Hence, forecast bias is lower (Panel A) and precision is higher when institutional

holdings are high. These results provide an important extension to the results in BPS [2016] and

Farboodi et al. [2017]. These authors argue that institutional owners are better at processing

information, and thus there is a positive relation between institutional holdings and price

32

informativeness. Our results show that better price informativeness in the presence of higher

institutional holdings manifests itself both in terms of decreased bias and improved precision. This

is consistent with the interpretation that higher institutional holdings lead to lower short-sell

constraints, and thus higher price informativeness.

The coefficients on , become insignificant in Panel C. This suggests that R&D

spending is not associated with precision. Moreover, taken together with the rsults in Panel A,

which show a positive association between R&D spending and bias, these results suggest that, for

our sample of firms, there is a negative association between R&D spending and price

informativeness—i.e., higher R&D is associated with higher bias. This is at odds with the results

in BPS and Farboodi et al. [2017], who find a positive association between R&D spending and

price informativeness for S&P 500 firms.

The coefficients on , are positive and highly significant across all

specifications, consistent with firm-specific uncertainty being associated with lower forecast

precision. Finally, the coefficients on the Fama-French factor loadings remain insignificant across

specifications, higher , is associated with higher precision and ex post dirty surplus

accounting is associated with lower ex ante precision.

Taken together, the evidence in Table 7 shows significant associations between disclosure

variables, the presence of analyst coverage, additional firm-environment variables and our metrics

of price informativeness. Importantly, our research design allows us to separately evaluate bias

and precision. Broadly speaking, we find that firms that provide more-disaggregated financial data

and longer filings have lower forecast bias and higher forecast precision, respectively. Similarly,

the presence of analysts and the intensity of their following are also associated with lower bias,

higher precision and higher price informativeness.

33

7. Conclusion

Price informativeness is a central economic phenomenon. When equity prices are more

informative, investors pay a fairer price for risk sharing and consumption smoothing, entrepreneurs

receive funding that is commensurate with their value-creation potential and economic agents learn

more from equity prices, which, in turn, implies that they make more-informed real decisions.

Hence, understanding what determines price informativeness is a central issue in accounting,

finance and economics.

In this study we shed some light on the determinants of price informativeness. To do that

we first propose a new measure of price informativeness. Our measure reflects the accuracy of the

levels of the expectations embedded in observed equity prices. Hence, it is intuitive yet rigorous.

Moreover, it can be used at both the firm- and economy-level and to separately evaluate forecast

bias, forecast precision and their combined effect.

Our empirical results show that economy-level price informativeness is high when: (1)

there is moderate investor sentiment (either positive or negative); (2) limits to arbitrage are low;

(3) uncertainty is low; (3) unemployment is low; and, (4) the aggregate earnings-to-price ratio is

high. Our firm-level tests show that firms have more informative prices when: (1) they provide

greater transparency in terms of more-disaggregated accounting data and/or longer 10-Ks or (2)

they have good information environments in terms of analyst following and the intensity of that

following.

34

Appendix A: Variable Definitions

Model variables:

Variable Definition Data Source

, Equity market value of firm i at the end of quarter t (see App. B) Compustat

, Earnings of firm i for quarter t (see App. B) Compustat

, Dividend paid by firm i in quarter t (see App. B) Compustat

, Book value of firm i at the end of quarter t (see App. B) Compustat

, 1 , where , is the quarterly risk-free rate (see App. B) US Fed, Compustat and CRSP

, 1 , where , is firm i’s quarterly cost of equity risk (see App. B) US Fed, Compustat and CRSP

, ∑ , , 1 , or firm i’s aggregate cum-dividend earnings for the time-period spanning quarter t+1 through t+T

Compustat, US Fed, CRSP

, , , , , or the change in premium of equity market value over book value for the time-period spanning quarter t+1 through t+T

Compustat

, Price informativeness for firm i at the end of quarter t, measured as

,,

,

, (see App. B)

Compustat, US Fed, CRSP

_ , Absolute value of , Compustat, US Fed, CRSP

Economy-level time-series analyses (time subscripts omitted):

Variable Definition Data Source BIAS ∑ , , calculated by quarter (see App. C)

Compustat, US Fed, CRSP

ABS_BIAS

_∑ , calculated by quarter (see App.

C)

Compustat, US Fed, CRSP

STD ∑ , ,

calculated by quarter (see App.

C)

Compustat, US Fed, CRSP

RMSE ∑ , calculated by quarter (see App. C)

Compustat, US Fed, CRSP

SENT Sentiment index from Baker and Wurgler (2007) Baker and Wurgler’s website: http://people.stern.nyu.edu/jwurgler/

35

ABSSENT Absolute value of SENT Baker and Wurgler’s website: http://people.stern.nyu.edu/jwurgler/

NOISE Monthly average of Hu et al. (2014) Noise index Jun Pan’s website (http://www.mit.edu/~junpan/)

SPVOL Monthly standard deviation of daily S&P 500 Index returns CRSP INDPROD Industrial production index Federal Reserve

economic data UNEMP Monthly unemployment rate US Dept. of LaborGDPGROWTH Quarterly GDP Growth, percent change from the previous

period, seasonally adjusted annual rateFederal Reserve Bank of St. Louis

BM Aggregate book-to-market ratio for all firms in the sample (see App. B for definition of equity book value and equity market value)

Compustat

EP Aggregate earnings-to-price ratio for all firms in the sample (see App. B for definition of earnings and equity market value)

Compustat

Firm-level cross-sectional analyses (firm subscripts omitted):

Variable Definition Data Source Firm-level measure of model variable ,

measured on a quarterly basis. Measured two quarters after the fiscal year end for year .

Compustat, US Fed, CRSP

_ Absolute value of , . Measured two quarters after the fiscal year end for year .

Compustat, US Fed, CRSP

DQt Firm DQ index per Chen et al. (2015). Authors of Chen et al. (2015)

FOGt Fog Index as defined in Li (2008). Feng Li’s website: http://webuser.bus.u

mich.edu/feng/FOLLOWINGt Indicator variable that equals one if the firm has

analyst following during the year and zero otherwise.

I/B/E/S

LNNUMFCSTt Log of (one plus the number of unique analysts with outstanding forecasts as of the end of the fiscal year).

I/B/E/S

SIZE10Kt Log of the 10K file-size as per Loughran and McDonald (2014).

https://sraf.nd.edu/

INSTITHOLDt Ratio of total shares held by institutions divided by

total firm shares outstanding at fiscal year-end.Thomson Reuters 13f Holdings

AVEFUTROEt Forecast of the conditional mean of , per Chang et al. (2018).

Authors of Chang et al. (2018)

SDFUTROEt Forecast of the conditional standard deviation of , per Chang et al. (2018).

Authors of Chang et al. (2018)

RDSALESt R&D expense scaled by total sales. Compustat

36

HML_FACTt Firm-specific Fama and French HML factor loading, estimated using a 60-months rolling window regression of firms’ monthly return on the monthly factors.

CRSP, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

SMB_FACTt Firm-specific Fama and French SMB factor loading, estimated using a 60-months rolling window regression of firms’ monthly return on the monthly factors.

CRSP, http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

DIRTt ( , , ∑ , , . Compustat

ABSDIRTt Absolute value of , . Compustat ROEt 4 ⁄ . is income and is

equity book value.Compustat

ROAt, 4 ⁄ . is income and is total assets.

Compustat

MARGINt ⁄ . is income and sales for the quarter.

Compustat

LEVERAGEt ⁄ . is total assets and is equity book value.

Compustat

t The residuals from the regression of on a set of control variables, industry fixed

effects and year fixed effects.

Compustat, US Fed, CRSP

_ The absolute value of Compustat, US Fed, CRSP

Appendix B: Calculation of , .

This appendix provides the detail on our calculation of , for each firm quarter in our

sample. ,

,,

,

,. In this equation, , is the equity market value of firm at the end

of quarter and , ∑ , , 1 , is firm ’ aggregate cum-

dividend earnings for the time period spanning quarter 1 through . , is

estimated as firm ′ realized earnings for quarter and , is estimated as the actual

dividend paid by firm at the end of quarter . , 1 , and , 1 , ; and,

, and , are the quarterly risk-free rate and the expected quarterly rate of return on firm ’ cost

of equity capital, respectively. We use 20 quarters, which corresponds to 5 years.

37

, is the quarterly net income and, depending on data availability, we use the one

of the following definitions, which are shown in order of preference: Compustat item IBCOMQ

(Income Before Extraordinary Items - Available for Common); or, IBQ (Income Before

Extraordinary Items) less MIIQ (Noncontrolling Interest - Income Account); or, NIQ (Net Income

/Loss) less XIQ (Extraordinary Items). If none of the above three options yields an earnings

number and if data is available for the other three quarters of the fiscal year, we impute the income

for the missing quarter using the annual income (IBCOM) for the corresponding fiscal year. If

IBCOM is also missing, but the income for the trailing three quarters are available, we estimate

the income for the current quarter as EPSX12 (Earnings Per Share (Basic) - Excluding

Extraordinary Items - 12 Months moving) times CSH12Q (Common Shares Used to Calculate

Earnings Per Share - 12 Months Moving) less the cumulative income for the trailing three quarters.

, is the product of DVPSXQ (Div per Share - Exdate – Quarter) and shares

outstanding at the beginning of the quarter CSHOQ (Common Shares Outstanding), adjusted for

stock splits etc. using AJEXQ (Adjustment Factor (Company) - Cumulative by Ex-Date). In case

the above is missing, 1/4th of the annual dividend (DVC) is used. If both are missing, the quarterly

dividend is set equal to zero.

We estimate the quarterly risk-free rate , using annual US treasury rates on zero coupon

bonds with maturities equal to 4 years. We derive the expected quarterly rate of return , for

each firm from the annual expected rate of return calculated as follows:

, = , ,

We estimate , as described above and maturity matched to the T/4-year treasury rate.

We use a market risk premium (MRP) of 5 percent. We estimate , for each firm in each

quarter by re-levering the respective industry un-levered beta. For un-levered betas we use the

38

Fama-French 30 industries. We estimate the raw industry beta for each industry-quarter using a

rolling 60-month window return and unlevered using trailing five-year industry average leverage.

We re-lever the un-levered industry beta using trailing five-year average firm leverage. We

calculate the equity market value of the firm at the end of each quarter, , , from Compustat as

PRCCQ (Price Close – Quarter) times CSHOQ (Common Shares Outstanding).

We calculate , for every firm-quarter for which we have a minimum of leading 4

quarters of non-missing EARN data and we use up to a maximum of 20 quarters (T/4=5 years). We

terminate our , estimation in 2011 as we have full Compustat data only through the fourth

calendar quarter of 2016. We identify delisting years from CRSP and all 4 quarters of such years

are excluded from the , as well as the EARN calculation. This implies that , is not

calculated for any of the quarters in the delisting fiscal year and that the last EARN values used for

any , calculation will be from the quarters one fiscal year prior to the delisting fiscal year.

For example, if a firm gets delisted in the fiscal year 2000, , will be calculated for this firm

up to the 4th fiscal quarter of the fiscal year 1998. The , estimate for the 4th fiscal quarter of

1998 will use 4 quarters of EARN from the fiscal year 1999. For firms which get temporarily

delisted but continue to trade subsequently (for example after a bankruptcy / restructuring etc.),

, is calculated soon after the delisting year and subject to both income and market value data

becoming available.

To account for violations of clean surplus accounting (i.e., “dirty” surplus) we calculate

the variable , , , ∑ , , . If clean surplus holds, the

difference between , and , will equal the cumulative difference between earnings and

dividends and , will equal zero. We use , as a control variable in our firm-level cross-

39

sectional regressions. Finally, we drop all observations with one or more of the following variables

missing from the final dataset: ERR, SALEQ, ATQ, LTQ and DIRT.

Appendix C: Calculation of Quarterly Economy-level Price-informativeness Measures

For our economy-level time-series tests, we calculate quarterly-level price informativeness

measures by aggregating firm-level values of , (see Appendix B) for each quarter. In

particular, we calculate the four statistics shown below:

∑ , (C.1)

_∑ , (C.2)

∑ , (C.3)

∑ , (C.4)

is the number of observations for quarter .

40

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43

Figure 1 Time-Series Graph of Biases (Unadjusted)

The figure shows the value of quarterly aggregate level price informativeness measure BIAS, ABS_BIAS, STD and RMSE, from 1975Q1 to 2011Q4.

See Appendix A for all variable definitions.

44

Figure 2 Time-Series Graph of Biases (Detrended)

The left figure shows the value of quarterly aggregate level detrended price informativeness measures BIAS and ABS_BIAS;

The right figure shows the measures STD and RMSE, from 1975Q1 to 2011Q4. We detrend all unadjusted variables in this analysis by separately regressing each of them on _ , and then using the residuals from these regression as our detrended variables of interest. See Appendix A for all variable definitions.

45

Table 1 Time-Series Analysis: Descriptive Statistics of Quarterly Price Informativeness Measures and Macro Variables

This table shows descriptive statistics for the variables used in the time-series analysis. Panels A and C present statistics for the unadjusted variables; Panels B and D present statistics for detrended variables. We detrend all unadjusted variables in this analysis by separately regressing each of them on

_ , and then using the residuals from these regression as our de-trended variables of interest. See Appendix A for all variable definitions.

Panel A: Price Informativeness Measures (Unadjusted)

Variable N mean sd min p1 p5 p10 p25 p50 p75 p90 p95 p99 max

BIAS 148 0.69 0.36 -0.48 -0.38 -0.16 0.07 0.63 0.78 0.88 1.03 1.10 1.15 0.34

ABS_BIAS 148 0.72 0.27 0.06 0.06 0.14 0.19 0.63 0.78 0.88 1.03 1.10 1.15 1.10

STD 148 1.08 0.40 0.61 0.62 0.68 0.71 0.82 0.98 1.24 1.62 1.99 2.52 0.32

RMSE 148 1.33 0.39 0.71 0.74 0.80 0.85 1.08 1.28 1.53 1.85 2.08 2.59 1.31

Panel B: Price Informativeness Measures (Detrended)

Variable N mean sd min p1 p5 p10 p25 p50 p75 p90 p95 p99 max

BIAS 148 0.00 0.26 -0.75 -0.64 -0.45 -0.40 -0.19 0.07 0.21 0.29 0.31 0.33 0.34

ABS_BIAS 148 0.00 0.22 -0.44 -0.43 -0.31 -0.25 -0.12 -0.03 0.06 0.31 0.44 0.78 1.10

STD 148 0.00 0.20 -0.41 -0.40 -0.36 -0.32 -0.16 0.04 0.17 0.22 0.24 0.29 0.32

RMSE 148 0.00 0.29 -0.61 -0.60 -0.39 -0.25 -0.17 -0.05 0.11 0.36 0.58 1.06 1.31

46

Panel C: Macro Variables (Unadjusted)

Variable N mean sd min p1 p5 p10 p25 p50 p75 p90 p95 p99 max

SENT 148 0.11 0.89 -2.20 -2.19 -1.74 -1.17 -0.25 0.15 0.62 0.91 1.26 2.41 2.83

ABSSENT 148 0.65 0.61 0.00 0.01 0.04 0.07 0.21 0.51 0.85 1.70 2.08 2.41 2.83

NOISE 101 3.63 2.16 1.29 1.33 1.45 1.98 2.38 3.21 4.34 5.58 6.02 11.71 18.38

SPVOL 148 0.01 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.01 0.01 0.02 0.03 0.03

INDPROD 148 73.83 19.44 41.61 42.97 48.32 50.18 56.21 68.15 93.77 98.78 102.11 105.09 105.13

UNEMP 148 6.47 1.62 3.90 3.90 4.30 4.50 5.30 6.05 7.40 9.00 9.60 10.30 10.80

GDPGROWTH 148 6.42 4.16 -7.70 -4.50 0.20 2.40 4.45 5.80 8.25 11.70 12.90 20.00 25.20

BM 148 0.56 0.20 0.24 0.24 0.27 0.32 0.39 0.52 0.74 0.87 0.92 1.01 1.03

EP 148 0.02 0.01 -0.03 0.00 0.00 0.01 0.01 0.01 0.02 0.03 0.03 0.04 0.04

47

Panel D: Macro Variables (Detrended)

Variable N mean sd min p1 p5 p10 p25 p50 p75 p90 p95 p99 max

SENT 148 0.00 0.85 -1.93 -1.93 -1.49 -1.15 -0.42 0.01 0.58 0.99 1.29 2.14 2.57

ABSSENT 148 0.00 0.56 -0.89 -0.82 -0.74 -0.67 -0.36 -0.07 0.26 0.75 1.05 1.92 2.33

NOISE 101 0.00 2.15 -2.08 -2.06 -1.95 -1.66 -1.20 -0.47 0.56 1.76 2.40 8.37 15.03

SPVOL 148 0.00 0.00 -0.01 -0.01 -0.01 0.00 0.00 0.00 0.00 0.01 0.01 0.02 0.02

INDPROD 148 0.00 5.30 -13.75 -11.61 -7.41 -6.62 -3.76 -0.36 4.21 6.70 7.81 10.69 11.18

UNEMP 148 0.00 1.59 -2.37 -2.36 -2.01 -1.66 -1.18 -0.41 0.62 2.75 3.44 3.93 3.97

GDPGROWTH 148 0.00 3.39 -10.81 -10.27 -4.72 -3.64 -1.95 0.05 1.82 3.59 4.36 10.65 15.29

BM 148 0.00 0.14 -0.24 -0.23 -0.21 -0.17 -0.10 -0.01 0.09 0.22 0.26 0.32 0.35

EP 148 0.00 0.01 -0.04 -0.01 -0.01 -0.01 0.00 0.00 0.00 0.01 0.01 0.01 0.02

48

Table 2 Time-series Analysis: Univariate Correlations between Detrended Price Informativeness

Measures

This table shows univariate correlations between detrended price informativeness measures used in the time-series analysis. We detrend all unadjusted variables in this analysis by separately regressing each of them on _ , and then using the residuals from these regression as our de-trended variables of interest. See Appendix A for all variable definitions. Pearson correlations at the bottom diagonal and Spearman correlations at the upper diagonal. The table shows the correlation coefficients with their corresponding p-values below in brackets. Bold values are significant at the 5% level.

BIAS ABS_BIAS STD RMSE

BIAS 0.74 0.09 0.03

(0.00) (0.30) (0.74)

ABS_BIAS 0.87 -0.50 -0.49

(0.00) (0.00) (0.00)

STD -0.54 -0.49 0.93

(0.00) (0.00) (0.00)

RMSE -0.22 -0.10 0.88

(0.01) (0.24) (0.00)

49

Table 3 Time-series Analysis: Univariate Correlations between Detrended Macro Variables

This table shows univariate correlations between detrended macro-variables used in the time-series analysis. We detrend all unadjusted variables in this analysis by separately regressing each of them on _ , and then using the residuals from these regression as our de-trended variables of interest. See Appendix A for all variable definitions. Pearson correlations at the bottom diagonal and Spearman correlations at the upper diagonal. The table shows the correlation coefficients with their corresponding p-values below in brackets. Bold values are significant at the 5% level.

(1) (2) (3) (4) (5) (6) (7) (8) (9)

(1)SENT -0.15 0.02 0.15 -0.02 0.09 0.01 0.08 0.01

(-0.12) (-0.83) (-0.06) (-0.77) (-0.27) (-0.91) (-0.30) (-0.86)

(2)ABSSENT 0.07 0.44 -0.21 -0.05 0.10 -0.33 0.04 -0.36

(0.37) (0.00) (-0.03) (-0.62) (-0.30) (0.00) (-0.68) (0.00)

(3)NOISE -0.20 0.03 0.08 0.03 0.08 -0.14 0.18 -0.11

(0.04) (0.75) (-0.35) (-0.67) (-0.34) (-0.09) (-0.03) (-0.17)

(4)SPVOL -0.01 0.11 0.64 0.01 -0.75 0.18 -0.28 0.02

(0.91) (0.19) (0.00) (-0.91) (0.00) (-0.03) (0.00) (-0.83)

(5)INDPROD 0.03 0.21 -0.24 0.01 -0.19 -0.25 -0.31 -0.29

(0.72) (0.01) (0.02) (0.89) (-0.02) (0.00) (0.00) (0.00)

(6)UNEMP -0.21 -0.01 0.15 0.06 -0.76 -0.19 -0.25 -0.31

(0.01) (0.87) (0.13) (0.50) (0.00) (-0.97) (0.00) (-0.01)

(7)GDPGROWTH -0.20 -0.04 -0.44 -0.24 0.18 0.01 0.03 0.29

(0.01) (0.65) (0.00) (0.00) (0.03) (0.86) (-0.68) (0.00)

(8)BM -0.29 0.03 0.26 0.22 -0.39 0.68 -0.05 0.71

(0.00) (0.75) (0.01) (0.01) (0.00) (0.00) (0.57) (0.00)

(9)EP -0.25 -0.13 -0.51 -0.25 -0.01 0.26 0.23 0.59

(0.00) (0.11) (0.00) (0.00) (0.92) (0.00) (0.00) (0.00)

50

Table 4 Time-Series Analysis:

Univariate Correlations between Price Informativeness Measures and Macro Variables This table shows univariate correlations between detrended price informativeness measures and macro-variables used in the time-series analysis. We detrend all unadjusted variables in this analysis by separately regressing each of them on _ , and then using the residuals from these regression as our de-trended variables of interest. See Appendix A for all variable definitions. Pearson correlations are in Panel A; Spearman correlations are in Panel B. The table shows the correlation coefficients with their corresponding p-values below in brackets. Bold values are significant at the 5% level.

Panel A: Pearson Correlations Panel B: Spearman Correlations

BIAS ABS_BIAS STD RMSE BIAS ABS_BIAS STD RMSE

SENT 0.69 0.52 -0.40 -0.26 SENT 0.59 0.46 -0.41 -0.23

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.01)

ABSSENT -0.38 -0.18 0.23 0.18 ABSSENT -0.39 -0.27 0.18 0.10

(0.00) (0.03) (0.00) (0.03) (0.00) (0.00) (0.03) (0.23)

NOISE 0.14 0.17 0.32 0.40 NOISE 0.32 0.25 0.28 0.41

(0.15) (0.10) (0.00) (0.00) (0.00) (0.01) (0.00) (0.00)

SPVOL 0.05 0.08 0.28 0.36 SPVOL 0.13 0.11 0.21 0.31

(0.54) (0.35) (0.00) (0.00) (0.12) (0.17) (0.01) (0.00)

INDPROD -0.02 0.05 -0.15 -0.14 INDPROD -0.09 0.04 -0.06 -0.09

(0.79) (0.55) (0.07) (0.08) (0.28) (0.66) (0.44) (0.28)

UNEMP -0.34 -0.37 0.29 0.17 UNEMP -0.28 -0.37 0.30 0.15

(0.00) (0.00) (0.00) (0.04) (0.00) (0.00) (0.00) (0.06)

GDPGROWTH -0.26 -0.25 0.04 -0.04 GDPGROWTH -0.26 -0.21 0.05 -0.04

(0.00) (0.00) (0.62) (0.61) (0.00) (0.01) (0.51) (0.60)

BM -0.43 -0.52 0.20 0.05 BM -0.41 -0.48 0.15 -0.11

(0.00) (0.00) (0.01) (0.58) (0.00) (0.00) (0.07) (0.18)

EP -0.38 -0.50 -0.13 -0.32 EP -0.45 -0.49 -0.08 -0.39

(0.00) (0.00) (0.11) (0.00) (0.00) (0.00) (0.34) (0.00)

51

Table 5 Firm-level Cross-sectional Analysis: Descriptive Statistics

This table shows descriptive statistics for the variables used in the firm-level cross-sectional analysis. See Appendix A for all variable definitions.

Variables N mean sd min p1 p5 p10 p25 p50 p75 p90 p95 p99 max ERRt 79382 0.81 0.96 -1.70 -1.16 -0.46 -0.12 0.30 0.68 1.13 1.91 2.63 4.40 5.74ABS_ERRt 79382 0.93 0.84 0.00 0.02 0.09 0.17 0.39 0.72 1.16 1.91 2.63 4.40 5.74DMERRt 79382 0.00 0.82 -4.17 -1.89 -1.16 -0.83 -0.40 -0.06 0.28 0.83 1.44 3.04 5.60ABS_DMERRt 79382 0.54 0.61 0.00 0.01 0.03 0.06 0.15 0.35 0.70 1.27 1.77 3.07 5.60

DQt 65745 0.60 0.11 0.25 0.39 0.43 0.46 0.52 0.58 0.66 0.77 0.80 0.87 0.92FOGt 31117 19.47 2.07 0.00 16.24 17.41 17.86 18.57 19.39 20.31 21.36 22.16 24.55 42.04SIZE10Kt 29229 13.58 1.12 6.79 11.55 11.95 12.15 12.62 13.66 14.34 14.91 15.39 16.50 18.77FOLLOWINGt 79382 0.48 0.50 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00LNNUMFCSTt 79382 0.73 0.90 0.00 0.00 0.00 0.00 0.00 0.00 1.39 2.20 2.48 3.00 3.93INSTITHOLDt 79382 0.34 0.29 0.00 0.00 0.00 0.00 0.06 0.28 0.56 0.78 0.88 1.00 1.00RDSALESt 79382 0.12 0.26 0.00 0.00 0.00 0.00 0.00 0.00 0.06 0.46 0.96 1.02 1.02SDFUTROEt 79382 0.11 0.11 0.00 0.01 0.01 0.03 0.04 0.07 0.14 0.23 0.32 0.54 1.20HML_FACTt 79382 0.00 0.01 -0.13 -0.02 -0.02 -0.01 0.00 0.00 0.01 0.02 0.03 0.03 0.16SMB_FACTt 79382 0.01 0.01 -0.11 -0.01 0.00 0.00 0.00 0.01 0.01 0.02 0.02 0.04 0.27AVEFUTROEt 79382 0.07 0.20 -1.32 -0.66 -0.30 -0.16 0.01 0.11 0.17 0.23 0.29 0.49 2.05DIRTt 79382 0.28 0.71 -0.72 -0.70 -0.30 -0.17 -0.03 0.06 0.34 0.93 1.58 3.89 4.55

52

Table 6 Firm-level Cross-sectional Analysis: Univariate Correlations

This table shows univariate correlations between the variables used in the firm-level cross-sectional analysis. See Appendix A for all variable definitions. Pearson correlations at the bottom diagonal and Spearman correlations at the upper diagonal. The table shows the correlation coefficients with their corresponding p-values below in brackets. Bold values are significant at the 5% level.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

(1) ERRt 0.88 0.05 0.10 0.05 -0.08 0.02 -0.01 0.00 0.21 0.40 0.03 -0.01 -0.41 0.00

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.30) (0.00) (0.00) (0.00) -(0.11) (0.00) -(0.78)

(2) ABS_ERRt 0.90 0.22 0.07 0.05 -0.07 -0.01 -0.05 -0.05 0.20 0.39 0.01 -0.04 -0.43 0.06

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.03) (0.00) (0.00) (0.00)

(3) ABS_DMERRt 0.41 0.64 0.04 0.03 0.00 -0.06 -0.08 -0.10 0.08 0.24 -0.01 -0.04 -0.27 0.16

(0.00) (0.00) (0.00) (0.00) -(0.98) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

(4) DQt 0.11 0.09 0.06 0.13 0.56 0.32 0.35 0.45 0.38 0.29 -0.02 0.00 -0.13 -0.12

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.47) (0.00) (0.00)

(5) FOGt 0.03 0.03 0.01 0.07 0.28 0.06 0.08 0.05 0.04 0.09 -0.03 0.08 -0.10 0.04

(0.00) (0.00) -(0.06) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

(6) SIZE10Kt -0.05 -0.05 -0.01 0.57 0.16 0.31 0.43 0.36 -0.03 0.02 -0.19 0.33 -0.01 -0.06

(0.00) (0.00) -(0.20) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.01) (0.00) (0.00) -(0.04) (0.00)

(7) FOLLOWINGt 0.00 -0.04 -0.07 0.36 0.05 0.35 0.75 0.51 0.17 0.09 0.00 0.01 0.04 -0.07

-(0.23) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.24) -(0.03) (0.00) (0.00)

(8) LNNUMFCSTt -0.04 -0.07 -0.08 0.37 0.08 0.46 0.85 0.59 0.16 0.06 -0.02 0.03 0.07 -0.09

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

(9) INSTITHOLDt -0.04 -0.08 -0.09 0.46 0.05 0.38 0.57 0.63 0.22 0.09 0.01 0.07 0.08 -0.20

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.04) (0.00) (0.00) (0.00)

53

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)

(10) RDSALESt 0.32 0.32 0.13 0.34 0.07 -0.03 0.14 0.12 0.12 0.28 0.06 -0.05 -0.22 0.03

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

(11) SDFUTROEt 0.36 0.38 0.26 0.18 0.06 0.03 0.01 -0.02 -0.01 0.36 0.04 -0.05 -0.48 0.05

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

(12) HML_FACTt 0.01 -0.01 -0.01 -0.04 -0.03 -0.17 0.02 -0.02 -0.01 -0.04 0.01 0.37 0.03 0.00

(0.00) -(0.12) -(0.14) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.01) (0.00) -(0.02) (0.00) (0.00) -(0.41)

(13) SMB_FACTt -0.02 -0.05 -0.04 -0.06 0.02 0.34 -0.04 -0.01 -0.01 -0.11 -0.06 0.25 0.04 -0.01

(0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.01) -(0.14) (0.00) (0.00) (0.00) (0.00) (0.00)

(14) AVEFUTROEt -0.41 -0.44 -0.27 -0.13 -0.06 0.00 0.05 0.09 0.10 -0.44 -0.64 0.02 0.05 -0.13

(0.00) (0.00) (0.00) (0.00) (0.00) -(0.94) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00)

(15) DIRTt 0.00 0.14 0.22 -0.13 0.03 -0.05 -0.11 -0.11 -0.19 0.06 0.08 -0.01 0.00 -0.12

-(0.21) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) (0.00) -(0.97) (0.00)

54

Table 7

Firm-Level Cross-sectional Analyses: Regressions

This table shows the results of the estimations of the following regression:

, , , , , ∑ , , , , ,

The dependent variables are , in Panel A; _ , in Panel B and _ , in Panel C, respectively. DISC is a vector of the following 5 variables: DQ, FOG, SIZE10K, FOLLOWING, and LNNUMFCST. CONTROL is a vector of 7 control variables. is industry fixed effects, and is year fixed effects. Standard errors are clustered by industry and year. See Appendix A for all variable definitions. The table shows coefficient values and corresponding robust t-statistics between brackets. Significance levels are indicated as follows: *** p<0.01, ** p<0.05, * p<0.1.

Panel A: Dependent variable: ERRt

(1) (2) (3) (4) (5) (6)VARIABLES ERRt ERRt ERRt ERRt ERRt ERRt

DQt -0.38** (-2.78) FOGt 0.00 (0.50) SIZE10Kt 0.02 (0.95) FOLLOWINGt -0.00

(-0.10) LNNUMFCSTt -0.02*

(-1.86)INSTITHOLDt -0.35*** -0.36*** -0.20*** -0.23*** -0.34*** -0.31***

(-6.03) (-5.83) (-3.81) (-4.19) (-6.02) (-6.12)RDSALESt 0.57*** 0.57*** 0.52*** 0.50*** 0.57*** 0.57***

(4.49) (4.61) (3.38) (3.33) (4.50) (4.53)SDFUTROEt 0.83*** 0.79*** 0.78*** 0.79*** 0.83*** 0.83***

(5.22) (4.81) (6.27) (6.90) (5.22) (5.22)HML_FACTt -1.08 -0.55 -1.88 -0.81 -1.08 -1.08

(-0.98) (-0.35) (-0.81) (-0.45) (-0.99) (-0.98)SMB_FACTt -1.34 -1.22 -3.34 -0.94 -1.34 -1.39

(-1.65) (-0.82) (-0.91) (-0.45) (-1.66) (-1.69)AVEFUTROEt -1.14*** -1.10*** -1.13*** -1.19*** -1.14*** -1.14***

(-17.58) (-16.00) (-15.47) (-14.68) (-17.78) (-17.80)DIRTt -0.03 -0.02 0.19** 0.21** -0.03 -0.03

(-0.51) (-0.39) (2.49) (3.09) (-0.51) (-0.50)Observations 79,382 65,745 31,117 29,229 79,382 79,382Adj. R-squared 0.265 0.243 0.258 0.261 0.265 0.265

55

Panel B: Dependent Variable: ABS_ERRt

(1) (2) (3) (4) (5) (6)VARIABLES ABS_ERRt ABS_ERRt ABS_ERRt ABS_ERRt ABS_ERRt ABS_ERRt

DQt -0.39*** (-3.26) FOGt 0.00 (0.28) SIZE10Kt 0.01 (0.28) FOLLOWINGt -0.03*

(-1.87) LNNUMFCSTt -0.04***

(-3.58)INSTITHOLDt -0.39*** -0.41*** -0.29*** -0.29*** -0.36*** -0.32***

(-7.67) (-7.68) (-5.36) (-5.04) (-6.71) (-7.00)RDSALESt 0.45*** 0.45*** 0.42*** 0.40*** 0.45*** 0.46***

(3.74) (3.90) (3.27) (3.15) (3.77) (3.81)SDFUTROEt 0.78*** 0.71*** 0.76*** 0.78*** 0.77*** 0.77***

(5.21) (4.65) (6.78) (7.46) (5.21) (5.23)HML_FACTt -0.49 0.41 -0.51 0.05 -0.50 -0.50

(-0.53) (0.33) (-0.24) (0.03) (-0.55) (-0.54)SMB_FACTt -1.27* -1.57 -3.83 -2.24 -1.31* -1.35*

(-2.05) (-1.23) (-1.09) (-1.35) (-2.09) (-2.14)AVEFUTROEt -1.05*** -1.03*** -1.05*** -1.10*** -1.05*** -1.04***

(-18.44) (-16.58) (-15.21) (-15.18) (-18.91) (-19.14)DIRTt 0.13*** 0.13*** 0.25*** 0.26*** 0.13*** 0.13***

(3.59) (3.49) (3.83) (4.41) (3.60) (3.60)Observations 79,382 65,745 31,117 29,229 79,382 79,382Adj.R-squared 0.274 0.251 0.278 0.281 0.274 0.275

56

Panel C: Dependent variables: ABS_DMERRt

(1) (2) (3) (4) (5)

VARIABLES ABS_DMERR

t ABS_DMERR

t

ABS_DMERRt

ABS_DMERRt

ABS_DMERRt

DQt -0.09 (-0.98) FOGt -0.00 (-0.54) SIZE10Kt -0.02* (-2.17) FOLLOWINGt -0.06***

(-6.33) LNNUMFCSTt -0.04***

(-5.59)INSTITHOLDt -0.30*** -0.27*** -0.23*** -0.23*** -0.21***

(-12.41) (-8.83) (-6.62) (-8.61) (-8.66)RDSALESt -0.04 -0.03 -0.04 -0.03 -0.02

(-1.00) (-0.89) (-0.95) (-0.72) (-0.66)SDFUTROEt 0.56*** 0.57*** 0.52*** 0.59*** 0.60***

(5.81) (4.85) (4.85) (6.77) (6.84)HML_FACTt 0.38 -0.04 -0.19 0.09 0.11

(0.57) (-0.02) (-0.12) (0.20) (0.24)SMB_FACTt 0.42 0.09 -0.06 0.31 0.30

(0.50) (0.04) (-0.06) (0.75) (0.74)AVEFUTROEt -0.42*** -0.46*** -0.47*** -0.42*** -0.41***

(-7.88) (-5.99) (-6.02) (-8.59) (-8.45)DIRTt 0.19*** 0.23*** 0.22*** 0.18*** 0.18***

(10.35) (9.28) (9.03) (10.00) (9.97)Observations 65,745 31,117 29,229 79,382 79,382Adj. R-squared 0.163 0.170 0.166 0.168 0.168